The tildes on the numerators signify that these numerators do
not have to be the same as the ones appearing in
Eq. (REF ), but as noted in Ref. [1]} these can
be kinematic numerators from a different theory. Given such a representation we may obtain
the corresponding gravitational amplitude simply by replacing
the color factor with the corresponding kinematic numerator,
\(c_i \rightarrow \tilde{n}_i \,,\) 
